Microwave filter



March 13, 1956 w. A; MiLLER MICROWAVE FILTER 4 Sheets-Sheet l Filed Aug.11, 195o March 13, 1956 W. A. MILLER MICROWAVE FILTER Filed Aug. 1l,1950 4 Sheets-Sheet 2 gza . INVENTOR WML/HM H. IWLLf/ j f am ATTORNEYMarch 13, 1956 w. A. MILLER 2,738,469

' MICROWAVE FILTER Filed Aug. 11, 1950 4 Sheets-,Sheet .Z

ATTORNEY March 13, 1956 w. A. MILLER 2,738,469

MICROWAVE FILTER Filed Aug. 11, 195o 4 sheets-sheet 4 'm6060105 l F lPomme? ufff/6 me #awww/M75,

United States Patent Oli cc 2,738,469 Patented Mar. 13, 1956 MICROWAVEFnJrER William A. Miller, Miller Place, N. Y., assigner to RadioCorporation of America, a corporation of Delaware Application August 11,1950, Seri-ai No. 178,3@4

The terminal years ofthe term of the patent to be granted has beendisclaimed 1 Claim. (Cl. S33- 73) This invention relates to microwaveguide filters and particularly to such filters in which interference iscaused between components of' the waves of the frequencies to berejected.

More particularly, the invention provides Vfor the splitting of thetransmitted waves in the waveguide of a microwave system into twocomponents at right angles to each other, transmitting the twocomponents of lthe waves down a waveguide of a critical length andhaving different indexes of refraction for the two components(birefringent) and recombining the two components at the end of H thepredetermined length of the birefringent waveguide section, where thecomponents of the waves of other than the pass-band frequency areeliminated by interference therebetween, and from which end of thebirefringent guide section the waves of the pass-band frequency or thefiltered waves are further transmitted.

The invention further provides for the combination of birefringentsections of waveguides in series with each other or with filter sectionsof other types, such as an interferometer filter, and in combinationwith phase Shifters and waveguide sections of other dimensions andcharacteristics and of predetermined lengths.

The obtaining of more highly selective filters has become more importantwith the increase in demands for the use of microwave apparatus. In somelocalities, the microwave transmissions have become so crowded that amore economical use of the available frequencies must be made. Thefrequencies must not only be accurate, but they must be controlledwithin definite and narrow limits of bandwidths. In some cases, such asfor example in the multi-transmitter use of a single antenna, highlydiscriminating filters are essential.

The principal object of the invention is to provide a microwave filterin which constructive interference is caused in the pass-band frequencywaves and destructive interference is caused between components of Wavesof other than the pass-band frequencies.

Another object of the invention is to provide a microwave lter of highdiscrimination that is independent of load conditions of the waveguidesystem.

Another object of the invention is to provide a microwave filter of highdiscrimination without introducing into the waveguide any extraneousmaterials, either insulating or conducting.

Another object of the invention is to provide a microwave filter of highdiscrimination in which are sections of waveguides that eect differentvelocities of propagation along their lengths of `components of the samewave.

` Another object of the invention is to provide a microwave filter ofhigh discrimination that includes a waveguide section having differentindexes of refraction in its two longitudinal or axial planes oftransmission.

Another yobject of the invention is to provide a microwave filter ofhigh discrimination that includes a tunable interferometer filtersection.

Other objects and advantages of ithe invention will'be 2 apparent fromthe following detailed description made with reference to theaccompanying drawings in which:

Fig. 1 is a view in perspective of a rectangular waveguide; i

Fig. 2 is a graph showing the relation of a so-called index ofrefraction in a waveguide to the ratio of (l) the wavelength of theradiation in air to (2) the critical Wavelength of the guide.

Fig. 3 is a view in perspective of afilter comprising two birefringentfilter sectionsin cascade;

Fig. 4 is a graph showing the relation of relative power transmitted bya filter to the wavelength of the' transmitted waves in air 0a);

Fig. 5 is a graph showing the relation of insertion losses expressed indecibels to the wavelength of the transmitted waves in air Ora);

Fig. 6 is a group of graphs showing the narrowing of the pass-band ofthe filter by adding filter sections in cascade;

Fig. 7 is a view in perspective of a polarizing interferometer filter;

Fig. 8 is a view in perspective of a quarter-wave birefringent waveguidephase shifter, with the sides of the guide sections parallel to eachother;

Fig. 9 is a view in perspective of a half-wave birefringent waveguidephase shifter;

Fig. 10 is a simplified view in perspective of the device of Fig. 8, butwith the sides of the birefringent quarterwave guide sections at anangle to each other;

Fig. 11 is a diagram of the electric vectors in the various sections ofthe device of Fig. 10;

Fig. l2 is a view in perspective of a portion of a quarter- Wave guiderotary-joint phase shifter; and

Fig. 13 is a view in perspective of a portion of a halfwave guiderotary-joint phase shifter.

Bz'refrngent guide filter Referring to Fig. 1, 1 is a rectangularwaveguide of width y in the direction of arrow X, of height x in thedirection of arrow Y and of length l in the direction of arrow Z. Theguide 1 is of such physicaltdimensions that it will supportsimultaneously the transmission of a TEoi mode of radiation along itslength (iZ) with its electric vector (Ex) perpendicular to the Xdirection of the guide and a TEm mode of radiation along its length (iZ)with its electric vector (Ey) perpendicular to the Y direction of theguide. The guide 1 thus has two mutually perpendicular dimensions inwhich the group velocities of the propagated radiation may be adjustedby controlling the x and/or the y dimensions of the guide. These X and Ydirections are defined as .the propagation axes or, more simply, theaxes of the guide. The guide, therefore, has two indexes of refractionfor waves propagated along the length of the guide, that is, the guideis birefringent. The index of refraction along the axes is real for aTEM mode if l equals or is greater than )w1/2 and imaginary if l equalsor is less than )wz/2, where ka is the wavelength of the radiation inair.

By definition:

where n is the index of refraction, Va is the velocity vof propagationin air and Vg is the group velocity in the guide.

For a TEoi mode in rectangular guides,

V tft-wier l im [l M) :i

where Ac is the critical wavelength of the guide.

In Fig. 2, there is plotted the values of lz over a range of values of,M1/kc from zero to 1.7. The graph is a plot of Equation 3 from which itwill be noted that for values of )w1/kc greater than unity, the valuesof n are imaginary, as indicated in the lower half Of Fi g. 2 by (j).

If x is greater than y (Fig. l), then nx is less than ny, where nx isthe index of refraction for propagation in TEor mode in the birefringentguide with the E vector perpendicular to the XZ plane of the guide andny is the corresponding index of refraction for the propagation in theguide with the E vector perpendicular to the YZ plane of the guide.

Referring to Fig. 3, 2 is a non-birefringent rectangular waveguideconnected to birefringent waveguide section 3 of dimensions .r1 and y1,respectively. The non-hire fringent guide, hereinafter referred to as apolarizer, is set at an angle of 45 degrees to both the x and y axes ofguide section 3. When a wave in guide 2 of TEoi mode is fed into guideSection 3, the wave will split into two components at right angles toeach other and each component will be propagated along guide section 3independently of the other. The index of refraction for the componentswill be nx and ny, respectively.

For the purpose of analysis, let it be assumed that xi is greater thany1, then 11X is less than ny.

If the length of guide section 3 in cm. is Il, then for the nx wave:

l1=11l1 cm. of air and for the ny wave,

li--nyli cm. of air The path difference between the wave components is:

(ny-nnb cm. of air and the retardation (p) becomes:

path difference lit p m i,

where n is the difference between the indexes of refraction of guidesection 3 in the x and y axes, respectively.

At the output end of guide section 3, there is connected a secondpolarizer 2', set at an angle of 45 degrees to the x and y axes 0f guidesection 3 and parallel to polarizer Z. Interference will take place atthis connecting point between the nx and ny components of the inputwaves.

The transmitted intensity (T) in polarizer Z will be:

where T is the relative power transmitted through polarizer 2', assumingunit amplitude or voltage or current input from polarizer 2.

It will thus be seen that the guide section 3 and the `two polarizers 2and 2 constitute a filter section and when such a section istransmitting waves of various wavelengths, the power at the output endof the filter section will be zero for all wavelengths such that for agiven length, l, of the birefringent guide section, the retardation p ism/ 2, where m' is an odd integer and the power at the output end of thefilter section will be a maximum where m is an integer.

Referring again to Fig. 3, the output end of polarizer 2' is connectedto birefringent guide section 3', the axes of polarizer 2 being set at45 degrees to both the x and y axes of guide section 3. Likewise, athird polarizer 2 is connected to the output end of guide section 3. Twofilter sections are thus connected in cascade,

If the detardations of the two filter sections are p1, and p2, therelative power transmitted T2 becomes:

and with m sections,

means a progressively continuing or a continuous product over allintegral values of m from unity to m.

lf it is desired to combine the filter sections to apply to a particularpass-band frequency, the length of the bircfringent guide sections, orthe indexes of refraction, or

both, must be so adjusted that the retardations of the various units areintegrally related. That is: p2=2prz ps=2p2; p4=2p3; etc. Therefore,p2=2p1; [13:49h {24:8171; etc.

This relation reduces to the equation:

17m=2m1p1 (7) When such a relation exists between filter sections, allmaxima passed by the first unit will be passed by the other sections incascade and all waves of intermediate wavelengths between the maximapassed by the first section will be reduced to practically zero.

lt will be noted that, in a filter made up of sections in cascade, thespacing between pass-bands is determined by the filter unit having theminimum retardation and the width of the pass-bands at the half-powerpoint (3 db down) is a function ef the filter section having the maximumretardation and a function of the number of sections in cascade.

If nx and ny are equal in all of the units, the retardation p may bevaried by changing the length l of the bircfringent guide sections inthe circuits. Also, for this condition the individual lengths of thebirefringent guide sections in filter sectons in cascade is:

where lm is the length of the birefringent guide section in the mthfilter section of the series, m is an integer, and

l1 is the length of the first birefringent guide section.

For the TEor mode:

The effect of dispersion (D) within the birefringent guide section ofthe filter, the Variations of the index of refraction with changes in M,may be determined by differentiating ,u with respect to M. D thenbecomes:

The effect of dispersion in the filter' of this invention is to reduceall maxima of frequencies higher than the passband frequency and tocrowd together all maxima of lower frequency. These latter maxima may beeliminated by making the polarizers 2, 2', ete., of such a width as willcut off these undesirable maxima.

Referring to Fig. 3, the dimensions of such a filter to pass l cm.radiation are as follows: xi=x2=x32x411 0.833 em.; y1=y2=y3=y4=0-562cm., cutoff wavelength (M) of polarizers 2, 2', 2, 2'", 1.05 cm.; 11:1cm.; 12:2 cm.: l3=4 cm.; 14:8 cm.; length of polarizer betweenbirefringent guide sections=1-0 cm.; nx=i.25; ity-:2.25, ,Ll-:1.

Figs. 4, 5, and 6 are graphs showing the operational characteristics ofthe filter defined hereinabove.

In plotting the graph in Fig. 4, relative power transmitted versus )tain cm., dispersion was taken into account by calculating the value ofretardation for each wavelength from the curve in Fig. 2. The effect ofmaking the critical wavelength of polarizers 2, Z', etc., equal to 1.05cm., is shown at the right end of the graph where waves having lengthsabovey 1.05 ein. are cut ofl.

In Fig. 5 is plotted a graph showing the relation of mamas@ for onewavelength, yother wavelengths can be providedv vffor by reducing orincreasing'allfthe dimensions of the original filter by aconversionfactor.

It will also benoted f that 'the dispersion within the filterincreaseswith' thefdifferencesbetween-'the indexes of refraction (u) ofthe two axes of the -birefringent guide section. 'It is apparent thatthe 'dispersion can be de creased by.. changing the values of theindex'of refraction and these changes maybe compensated for by changingthe length of the birefringentl guide section.

lFrom the graphs ofFig. 6, which'were'prepared" from I*the operation" of'the kfilter of Fig. 2 built tor-pass waves of 30,000 mc., the width vofthe passebandat `db down iis 1000 rnc. With three sections inI cascadethe bandlwidth is 200 rnc. and withfour'- sections in series thebandwidth -is230 mc.

Polarizng. interferometer guide filter `In the `usevof the'tilterinfF-ig. 3, in someiwaveguide s'systerns, it .mayunot` be; practicalbecause ofspace condi- Vtions to incorporate into the'flter a sufficientnumber of 'iunitsr'thereof to `obtain the vdesiredrnininium width lofthe pass-band. Thus, in the'example ofa tilterin Fig.`3, the dimensionswereso chosen that the physical lengths of the filter units weremultiples (1, 2,-42and'8) of the nfree-'space wavelength Vat thetransmission maximum.

sectionfas will hereinaftertbe.described,'maybe used in combination withthe birefringent lter sections. For example, four vbirei'ringentguideunits `may'be used in -cascade=with `one `or vmore interferometeriguide'lter `-sections.4

-'Referring to'Fig.V 7,` 4 Lis a rectangularwaveguide trans-*-4=mitting-waves, in Va TEui mode, one frequency of which Iiitlis-desiredto'befpassed 'throughfthe filter. Guide 4 is connected-tosquarefguidefsectioniwith the sides of lguide-4 at an `angle of 45 -tothe sidesof `guide `5. 'A Awave, launched by'the rectangularguide 4, is-divided into two components polarized `at right angles to each otherlby passagethrough-"the'grating 6. `The said4 two `components, still *inthe-same vphase relation, enter a second square guide section7 and passtherethrough until they reach a secondfwire gratings. Grating`8 ismounted at an angle of 45 degreesl to vthe longitudinalaxes-'of,guide"7.

1Grating'8 reflects upward into guidevsec'tion the .waves'ofr thecomponent 'the electric vector of which is -parallel to" the wires of`thegrating 8. 'Guide-9v is shortcircuited by an end plate 10 whichreflects the waves in 1 guider-back to screen"8 whence they arevreflected back f toward: screen 6.

eln'themeantime, waves of `the other component, the

component the ,electric vectorfofr-which Vis'perpendicularl fponents`ofthe-:waves reflected by plates 10 and 11. The pathdifference (p)between these waves is twice the diierence between the lengths of guide7 (la) and guide 9 (Z4). If guide 7' has an index of refraction ofns andguide 9 has anindex of refraction of n4,

and ztheupower transmitted (T) is:

T=eos2 Q (nazi-m1,) (12) It is apparent that the retardation, p, may bereadily .adjusted by adjusting-the relative lengths of la and I4. Thismay be done by inserting conventional movable tuning plugs in the endsof the guides 7 and 9, respectively.

The waves that do not suffer destructive interference are reflected bygrating 6V into guide 12 and hence into output guide 13.

-Guides`7 and 9 are shown as square with transition sections connectingthem intorectangular guides. Both guides -7 and-9 may. be either squareor rectangular, but if rectangular, the two guides are positioned at 90degrees with respect to'each other.

Phase shifting between filter sections adjusting g rvto such a valuethat (p-l-g) for each lter section is an integer. from an examination ofEquation `13, it will ,be seen that this factor (p-l-g) may be made ,toVequal an integer if g can be varied in value from -1/2 to -l-l/z.

Phase shifter for rectangular waveguides 'Heretofore, phase shiftersforwaveguides have either been of the'fpinc section or sliding or linestretching Ltype, in which one section of a waveguide is lengthened withrespect to another waveguide section or of the rotating type in whichone, section 4of the waveguide is rotated about itslongitudinal axis inrelation to another similar sectionof waveguide. The latter type hasbeen limited in itsiusetoround waveguides and to the modes ofpropagation that require such round guides.

As the v`filter of this invention includes birefringent waveguidesectionsthat are rectangular in cross-section,

.a new construction of rotating phase shifter has been devised. Thephaseshifter includes in combination two sections of square waveguidesrotatable with respect to each other and without `loss of transmittedenergy, connected to two birefringent guide sections by short transitionsections. This combination of guide sections forms a section of awaveguide filter adapted to shift the phases of the polarized componentsof a wave propagated down .a waveguide system.

`Two types ofthe new phase Shifters will be described,

.both of vwhich depend. inV their operationen the relative `In one typeof phase shifter, ythe birefringent guide sections are'of such lengthsas to cause retardations of onequarter wavelength between the twoseparated compo nents 4of a wave therein. Such birefringent guidesections aref-designated herein asquarter-wave guides, or more denitelyquarter-wave retardation guides. Two quarterwave retardation guides Withtwo relatively rotatable square guide sections therebetween isdesignated as a quarter-wave phase shifter.

ln the second type of phase shifter, a rotatable birefringent guidesection is inserted between two quarterwave guides by two rotary phaseShifters. The inserted birefringent guide section is of such length asto cause retardations between the separated components of a wave thereinof one-half Wavelength and is designated as a half-wave guide. Likewise,a unity-wave guide section is twice the length of a half-wave guidesection and a two-wave guide section is twice the length of a unitywaveguide section. The half-wave guide with the two quarter-wave guides andassociated rotary phase shiftcrs is designated as a half-wave phaseshifter. ne embodiment of each of these types of phase Shifters areshown in Figs. 8 and 9 respectively.

Referring to Fig. 8, 4 is a standard waveguide for feeding radiation atan angle of 45 degrees into quarter-wave guide section 5. The directionof the electric vector of the waves transmitted in guide section 4 isindicated by the arrow y. Guide section is connected to square guidesection 13 by transition guide section 14.

Similarly, for the output end of the phase shifter, the output standardguide section 4 is connected to quarterwave guide section 5. Guide 5 isconnected to square guide section 13 by transition guide section 14.

The two square guide sections 13 and i3 are connected together by arotatable joint consisting of flanges or rings 15 and 16 which aresecured, respectively, to guide sections i3 and 13'. Ring l5 is hollowedout at 17 and near the rim of ring 15 is a holiowed groove i5 that isone quarter of a wavelength deep. This groove lS acts as a choke toprevent the energy transmitted through the square guide sections fromleaking out through the space between rings 15 and 16.

The direction of the electric vectors of the two coniponents within thequarter-waveguide 5 is indicated by the arrows r and s respectively.

ln Fig. 8, the sides of the two square guide sections l and 13 are shownas being parallel. There will, therefore, be no shifting of the phase ofthe two components and the electric vectors of the components inquarter-waveguide section 5 will be parallel, as shown by arrows s andr', respectively, to electric vectors s and r, respectively. Theelectric vector y' of the recombined components in the standard guidesection 4 will therefore be parallel to y.

A small amount of phase shift may be introduced by the transition guidesections i4 and 14', but such a shift of phase may be compensated for byadjustment in the length of the quarter-waveguide sections 5 and 5. Thatis, in determining the lengths of the quartenwave sections 5 and 5',consideration is given to the slight birefringent et'ect of transitionsections i4 and ld and the quarter-waveguide sections 5 and 5 areaccordingly adjustcd in length to correct for this condition.

From the symmetry of construction, it is apparent that the unit iscompletely bilateral and the input and output ends may be interchangedwithout affecting the operation of the device.

ln the operation of the device in Fig. 8, guide section 4 may be rotatedabout its longitudinal axis with respect to guide section 4. lf guidesection 5' is rotated with respect to guide section 5 and guide section5 is clamped to guide section 4, guide section 4' and all other guidesections to the right of guide section 4 must also be rotated. ln sonicinstallations it may be inconvenient to rotate the guide sections to theright of the device. For such installations, there is provided ahalf-wave phase shifter in which a section of birefringent waveguide isinserted between the two square guide sections and of such length as tocause a relative retardation between the two components in thebirefringent waveguide section `of one-half wavelength of thetransmitted waves.

Such a construction is shown in Fig. 9.

In Fig. 9, rings and 16 are connected, respectively, to square guidesections 13 and 13 and form rotatable joints between the two pairs ofsquare guide sections 13 and 13. Between this pair of jointed squarewaveguide sections are the birefringent half-waveguide section 19 andthe interconnecting transition sections i4 and i4. The outer ends of thejointed square wave sections are connected to quarter-waveguide sections5 and 5', which are connected, respectively, to the ends of the standardwaveguide sections 4 and 4.

Fig. 10 is a simplified drawing of the device of Fig. 8 with the twojoint-coupled symmetrical sections thereof positioned at an angle p toeach other. Twenty is a guide section corresponding to quarter-waveguidesection 5, transition section 14 and square guide section i3 of Fig. 8.Twenty-one (21) is a guide section corresponding to square guide section13', transition section 14 and quarter-waveguide section 5 of Fig. 8.Sections 2) and 2li are connected respectively, to standard linear guidesections 4 and 4. The lengths of sections 20 and 2l are such that therelative retardation p of the two components of the waves transmittedtherein is equal to vr/Z, that is, they are quarter-waveguides. In Fig.8, y indicates the direction of the electrical vector in the linearwaveguide 4 transmitting a TEoi mode wave, and s and r indicate thedirections of the electrical vectors, respectively, of the twocomponents of the wave in section 2Q. s and r indicate the directions ofthe electrical vectors, respectively, of the two components of the wavein section 21 and y indicates the direction of the electrical vector ofthe recombined wave components in guide section 4.

The relative positions of the electrical vectors are shown in Fig. 1l inwhich corresponding letters and primed letters are applied.

It will be noted in Fig. ll that r', s', and y are all displaced, by theangle p, from r, s, and y, respectively. It will also be noted that rand s are mutually perpendicular to each other and each is at an angleof degrees with respect to y. Likewise, r and s are perpendicular toeach other and each is at an angle of 45 degrees with respect to y.

Operation of the quarter-wave phase shifter As indicated hereinbefore,the property of a quarterwaveguide, which makes it useful for thepurpose of phase shifting, is that it will transform linearly polarizedradiation to circularly polarized radiation components, provided thatthe guide is fed by a rectangular waveguide in which the plane of theelectrical vector of the linearly polarized radiation is at an angle of45 degrees to two mutually perpendicular allowable planes oftransmission in the quarter-waveguide and provided that thequarterwaveguide is fed with a radiation of such a frequency that therelative retardation between the two components during the travel of thecomponents along the quarter-waveguide is one quarter of the wavelengthof the radiated wave. The necessary construction conditions are met bydetermining the physical lengths of the quarter-waveguide, havingconsideration for transition sections if any are required for squareguide rotatable joint sections, and by determining the indexes ofrefraction by adjusting the physical dimensions of the sides of thequarter-waveguide section.

Referring again to Figs. l0 and 11, y and y are the didirections of theelectrical vectors in the feed guide 4 and 4', respectively. ln theanalysis that follows, the subscript (b) applied to an electrical vectorindicates the position of the vector at the beginning or source side ofthe guide and the subscript (e) indicates the position of the vector atthe end or sink side of the guide. By this nomenclature, rb and sb arethe electrical vectors at the beginning and re and se are the vectors atthe end of the 9 first quarter-waveguide, section 20. fb and s'b are theelectrical Vectors at the beginning and r" ands'e are the vectors at theend of the second yquarter-waveguide, section 21.

It will be noted that rb and re have the same space orientation as r,and sb, se and s have the same space orientation.

If it be assumed that components (and s) is the more retarded componentin the birefringent guide section, the r vectors may be chosen asreferences when measuring the relative phases between the vectors. rbtherefore equals re and r'b equals re, both for the quarter-Waveguideand the half-waveguide. For the quarter-waveguide, se is 11-/2 behind sbin phase and se-is 1r/2 behind s'b in phase. v

For the half-waveguide, ve is 1r behind vb in phase and ub equals ne,where ,u and v replace r and s, respectively, as used in connection withquarter-waveguides.

If (a) is the amplitude of the E vector in the feed guide 4, and itextends in the y direction and rif t is time and f is the frequency ofthe transmitted wave, the radian velocity (1w) equals 21rf and y=a sinwt (16) Resolving y along r and s at the beginning of the rstquarter-waveguide,

rb=j" sin wt (17a) and . a n i s1,=- sin wt (17b) At the end of thefirst quarter-wave section the s vector has been delayed `1r/2 radianswith respect to lthe r vector and These two waves, withelectricaLvectors fre and se, then pass into an exactly similarquarter-waveguide which has been rotated about its longitudinal axis byan angle p with respect to the first quarter-waveguide. Thus:

r11- 1re cosfp-se sin p (19a) and Substituting the value of 4re and se.in Equations 18a and 18b in Equations 19a and 19b,

At the end ofthe second quarter-waveguide rb=r' and and a sin tw/2 (w P)Analyzing E along y', which is at an angle of 45 degrees to both r ands',

y'=a SIl (wt-p) (22) Comparing Equations 16 and 22, it is seen that withthe rotation of one section 21 of the device of Fig. 10 with respect tothe other section (20) by an angle p, the amplitude of the E vectors isnot changed, but the phase of the E vectors has been shifted through anangle of p, These two conditions are both necessary and sufficient forthe operation of a phase shifting device.

The device is equally effective as a phase shifter when a heterogeneouswave beam is applied, such as might be produced by properly exciting asquare waveguide and connecting it to the birefringent quarter-waveguidesection 20, Fig. l0.

As an example of the determining of the dimensions of the phase shifterof Fig. 1() for a transmitted wave of 1.0 cm., the indexes of refractionmay be assumed as nf=l.1 and ns=1.8. The width of the r side, the sideof the birefringent section to which the r component is perpendicular,and the width of the s side may be determined from Fig. 2. The valuesare found to be r=2 cm. and s=0.605 cm.

Referring to Equation 4,

For a half-waveguide, l would be twice 0.357 or 0.714 cm.

The square guide section should have a length of about 1/2 or 1wavelength or between 0.5 crn. and 1.0 cm. The transition sections 14and 14 need be only a convenient small fraction of a wavelength. Thechoke groove 18 in the joint ring 1S must be approximately M 4. Thewidth of the groove is not critical, if it is less than 8. The overalllength for the phase shifter for \=1 cm. is approximately 3.5 cm. Forconstant values of nr and ns the length of the phase shifter isproportional to the wavelength.

Operation 0f half-wave phase shifter Referring to Fig. 9, when the phaseshifter is fed by a linear polarized wave through guide 4,

y=a sin wt (26a) and With the angle p between the quarter-waveguides 5and S equal to zero, and the guides 5 and 5 maintained fixed in theserelative positions, the half-waveguide 19v is rotated through go degreesabout its longitudinal axis, which is an extension of the axes of 4, 4',5, 5", 13 and 13. The mutually perpendicular axes of the components ofthe resolved waves in the half-waveguide section 19 are designated as uand v respectively. These axes correspond to r, r', and s, s',respectively, of the quarterwaveguide sections 5 and 5'.

`9, a rotation of the The resolved electrical vectors at the exit end ofthe quarterwaveguide 5 have been defined as r,= sin wt (isa) and (lsecos wt (1811) With the half-waveguide 19 rotated go degrees withrespect to quarter-waveguides 5 and 5', the resolved vectors about theI.' and v axes become:

11b=re cos p+sa sin tp (27a) rb=r sin p-sc cos (p (2711) uFgrsin (www)(esa) v '--qcos (wt-lb x/ P As there is a Jfurther phase shift of fradded to the vb vector to obtain the ve vector,

Resolving these components on the r and s' axes, which are displacedbackward from n and v by the angle (p,

rbruc cos f/-re sin rp (30a) sb=-ue sin (p-ve cos ip (30h) T'Fisin(wt-2a) (31a) 35:3: cos (wz-2s) (sib) and 7",= sin (w2 p) (32a)SAF-assis (apap) (g2b) vJet/"Goff en@ Z/=(l Siti (wi-2in) ComparingEquation 33 with Equation 26a, it is seen that the amplitude of thewaves has bcn preserved, but that for a rotation of cp degrees of thehalf-waveguide 1%, introduces a phase shift of 25a degrees.

An analysis may be made of the relation between vectors when aheterogeneous beam is applied to the halfwave phase shifter in Fig. 9 ascan mede for the quarter-wave phase shifter in Fig. S. lt will be foundthat when a heterogeneous beam, such as might be produced by properlyexiting a wa eguide of square cross section, is transmitted through thehalf-wave phase shifter in Fig. r-wawegin'dc of p degrees will produce aphase shift of 4p.

In applying the invention disclosed herein to particular installations,a considerable range of selection of filter sections is available. lftuning is not required in tthe installation, a single filter sectioncomprising me feed guide section 2, birefringent section 3 and polarizer2', shown in Fig. 3, may be used. However, as pointed out herein, thebandwidth of the filter is progressively narrowed by adding furtherfilter sections in cascade. (See Fig. 6.) In such a cascade arrangement,the interferometer filter section (see Fig. 7) may be inserted, theinput guide section 4 being connected to the output of polarizer section2 and the output guide section 13 being connected to the input ofbirefringent guide section 3 (Fig. 3),

Where tuning is desired, either one of the two types of birefringentrotary-joint phase shifter sections may be used, such as are shown inFigs. 8 and 9, or any other type of phase shifter may be used.

In applying these phase Shifters to an installation, both of thequarter-waveguides at the ends of these Shifters can not be used both asa filter element and a phase shifter element due to the fact that apolarizer must be inserted between otherwise adjoining birefringentguide sections. Thus, in a filter made up of birefringent guide sectionsand phase Shifters, the input of the phase shifter unit is aquarter-waveguide section but the length of the output end of the phaseshifter unit depends upon its relative position in the cascade. As anexample, the output end of the first phase shifter in a filter of unitsin cascade will be twice the length of the first birefringent guidesection and the length of the output end of the second phase shifterwill be twice the length of the output end of the first phase shifter.

Portions of such filters are shown in Figs. l2 and 13, in which thevarious sections are labeled.

As conventional movable tuning plugs may be substituted for the shortingplates 10 and 11 in the interferometer filter section in Fig. 7, such asection may be inserted in cascade with rotary-joint birefringent guidefilter sections.

As between the two types of rotary-joint birefringent phase Shifters,the half-waveguide type has the advantage of the independent rotating ofa filter section without disturbing the positions of the other filtersections. When the quarter-wave filter sections are used, the sectionsprogressively along the filter must be rotated an amount equal torotations of the previous sections and in addition the amount ofrotation required for the individual section.

There has thus been disclosed a microwave filter in which thetransmitted waves in a guide system are resolved into two components atright angles to each other. The two components are then transmitted downa waveguide section having the physical properties of retarding onecomponent with relation to the other component, such that at a criticaldistance from the input end of the waveguide section the components,when combined, suffer interference. Waves of undesired frequencies areeliminated by this interference while waves of a narrow bandwidth passthrough the filter. Two types of retarding guide sections, birefringentand interferometer, are assembled in cascade respectively or incombination, or each in combination with rotary phase Shifters and theirassociated birefringent sections.

What is claimed is:

A microwave filter for selectively transmitting mier wave energy over arange of operating frequencies comprising, a quarter-wave retardationguide section which is birefringent over said operating range offrequencies, a half-wave retardation guide section which is birefringentover said operating range of frequencies, means for impressing on saidquarter-wave retardation guide section a wave consisting of two equalplane polarized components polarized at right angles to each other withone component retarded one-quarter guide wavelength with respect to theother component, a polarizer connecting said quarter-wave guide sectionand said half-wave guide section, and a polarizer connected to theoutput end of said half-wave guide section, said polarizers eachcomprising a hollow pipe waveguide having broad and narrow walls with alongitudinal axis and dimensioned in the directions normal to said axisto have one and only one mode of propagation having a principal electricvector in one of said dimensions over said range of operatingfrequencies, the polarizers being connected to said quarter-waveretardation guide section and said half-wave retardation guide sectionwith the broad Walls of lsaid polarizers oriented at angles of 45 to theplanes of polarization of said two equal components.

References Cited in the le of this patent UNITED STATES PATENTS BowenSept. 13, 1938 Carter Sept. 5, 1944 Ring Aug. 12, 1947 Fox Mar. 23, 1948Stiefel Aug. 30, 1949

